How do we represent a $3$D vector? Here is some background.

Coordinate Direction Angles:

As seen, the transition to $3$D thus far has been quite simple, with the only modification to both the CVN notation, magnitude and unit vectors being the additional component Complexity starts to arise when we explore the angles a $3$D vector makes with the positive axes, called the coordinate direction angles:

k$)$ Coordinate direction angles allow for the easy calculation of vector components:

$F_x=|vec(F)|cos()$

$F_y=|vec(F)|cos()$

$F_z=|vec(F)|cos()$

Note: These angles are between $0$ and $180$ so the cosines may be $((+)$ or $(-)!$

Allows for negative components

Now, we will find the $500N$ force projected in the direction of $P$ using the dot productWhat is the projected force F$\_("\_")$P in the direction of P with $4$ digits after the decimal point?